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### High School Mathematics - 24.10 Introduction to Functions

 Function Definition: A function is a relation that has exactly one "output" for every "input". Consider two sets A and B to form the Cartesian product. This Cartesian product forms the relations. Among these relations we select those relations that satisfy the condition - every element on A is related to only one element in set B. When a relation satisfies this rule we call it function. Function: Any relation on A x B in which in which every element in set A has a corresponding element on set B. It is denoted as f: A ->B or f: x -> f(x) or y = f(x) where y is a function of x. First element is also called domain, abscissa, preimage or the first component. Second element is also called range, ordinate, image or second component. A function can be represented by arrow diagram, set-builder notation, Cartesian form. Representation of a function Arrow Diagram Domain = {1,2,3,4} Range = {D,B,C,A} Set-builder Notation f = {(x,y)ly = 3x+5} Cartesian Form f = {(1,2), (2,3), (4,5)} Directions: Solve the following problems. Also write at least 5 examples of your own.
 Q 1: If n(A) = p and n(B) = q, then the possible number of mappings from A to B is n?.0qp Q 2: Given that f(x) = 2x and f: N->N, find the range f .Answer: Q 3: Let X = {1,2,3,4}. Determine whether r not each relation is a function from X to X.g = {(3,1), (4,2), (1,1)}h = {(2,1),(4,4), (3,4)}f = {(2,3), (1,4), (2,1), (3,2), (4,4)} Q 4: Write the domain of h: x-> 2/(x-7)Domain is set of all real numbersDomain is all numbers except 7Domain is set of all natural numbers Question 5: This question is available to subscribers only! Question 6: This question is available to subscribers only!